Impulse and Change in Momentum quiz with answers for AP Physics C

📚 Quick Study Guide

• ⚖️ Impulse is the change in momentum of an object. Mathematically, it's expressed as $J = \Delta p = p_f - p_i$, where $J$ is impulse, $p$ is momentum, and the subscripts $f$ and $i$ denote final and initial values, respectively.
• ⏱️ Impulse is also equal to the average force applied over a time interval: $J = F_{avg} \Delta t$.
• ➡️ Momentum ($p$) is the product of an object's mass ($m$) and velocity ($v$): $p = mv$. Momentum is a vector quantity.
• 💥 The law of conservation of momentum states that the total momentum of a closed system (no external forces) remains constant: $\Sigma p_i = \Sigma p_f$.
• 🤝 In collisions, momentum is conserved. Kinetic energy may or may not be conserved. If kinetic energy is conserved, the collision is elastic; otherwise, it's inelastic.
• 🚀 Coefficient of restitution (e) quantifies the 'bounciness' of a collision: $e = \frac{\text{relative speed of separation}}{\text{relative speed of approach}}$. For perfectly elastic collisions, $e = 1$; for perfectly inelastic collisions, $e = 0$.
• 🔄 For variable forces, impulse can be calculated as the integral of force with respect to time: $J = \int F(t) dt$.

Practice Quiz

1. A 2.0 kg object moving at 3.0 m/s collides with a 1.0 kg object initially at rest. If the objects stick together after the collision, what is their final velocity?
   1. 1.0 m/s
   2. 2.0 m/s
   3. 3.0 m/s
   4. 4.0 m/s
2. A ball of mass $m$ is dropped from a height $h$ onto a stationary floor. If the coefficient of restitution between the ball and the floor is $e$, what is the speed of the ball immediately after the first bounce?
   1. $e\sqrt{2gh}$
   2. $\sqrt{2gh}$
   3. $e^2\sqrt{2gh}$
   4. $2gh$
3. A rocket expels exhaust gases at a rate of 20 kg/s with a velocity of 1.5 x 10^3 m/s relative to the rocket. What is the thrust force on the rocket?
   1. 1.0 x 10^3 N
   2. 3.0 x 10^4 N
   3. 1.5 x 10^3 N
   4. 3.0 x 10^3 N
4. A 0.5 kg ball is thrown against a wall with a velocity of 10 m/s. The ball rebounds with a velocity of 8 m/s. If the ball was in contact with the wall for 0.05 s, what was the average force exerted on the ball by the wall?
   1. 20 N
   2. 180 N
   3. 200 N
   4. 2 N
5. A system consists of two objects with masses $m_1$ and $m_2$ moving with velocities $v_1$ and $v_2$ respectively. What is the total momentum of the system?
   1. $m_1v_1 + m_2v_2$
   2. $m_1v_1 - m_2v_2$
   3. $\frac{1}{2}(m_1v_1^2 + m_2v_2^2)$
   4. $\sqrt{m_1^2v_1^2 + m_2^2v_2^2}$
6. A force $F(t) = 3t^2 + 2t$ (in Newtons) acts on a 2 kg object for 2 seconds, starting from rest. What is the change in the object's momentum during this time?
   1. 4 kg m/s
   2. 8 kg m/s
   3. 12 kg m/s
   4. 16 kg m/s
7. A 5 kg object is initially moving at 6 m/s. After an impulse is applied, its velocity changes to 8 m/s in the opposite direction. What is the magnitude of the impulse applied?
   1. 10 Ns
   2. 40 Ns
   3. 70 Ns
   4. 14 Ns